Question

a contract is good in the base of a circular fountain on the blueprint the base of the food has a date diameter of 18 cm the book has the skill address it to me and so forth see what will be the actual area of the base of the fountain and the squares the fda is blue to the nearest 10th of a square foot

Answer 1

Answer:  $452.4\ ft^2$

Step-by-step explanation:

The complete exercise is "A contractor is building the base of a circular fountain. On the blueprint, the base of the fountain has a diameter of 18 centimeters. The blueprint has a scale of three centimeters to four feet. What will be the actual area of the base of the fountain, in square feet, after it is built? Round your answer to the nearest tenth of a square foot."

The following formula can be used for calculate the area of a circle:

$A=\pi r^2$

Where "r" is the radius of the circle.

Let be "x" the actual diameter in feet of the base of the fountain.

You know that the  blueprint has a scale of  $3\ cm:4\ ft$, then, you can set up the following proportion:

$\frac{4}{3}=\frac{x}{18}$

Solving for "x", you get:

$(18)(\frac{4}{3})=x\\\\x=24$

Since the radius of a circle is half its diameter, you know that the actual radius  of  the base of the fountain is:

$r=\frac{24\ ft}{2}=12\ ft$

Now you can substitute the radius into the formula in order to calculate the actual area of the base of the fountain. Rounded to the nearest 10th, this is:

 $A=\pi (12\ ft)^2=452.4\ ft^2$